Difference between revisions of "Jadhav Prime Quadratic Theorem"
(→Historical Note) |
(Proposed for deletion) |
||
| Line 1: | Line 1: | ||
| − | In Mathematics, '''Jadhav's Prime Quadratic Theorem''' is based on | + | In Mathematics, '''Jadhav's Prime Quadratic Theorem''' is based on [[Algebra]] and [[Number Theory]]. Discovered by an Indian Mathematician [[Jyotiraditya Jadhav]]. Stating a condition over the value of <math>x</math> in the [[quadratic equation]] <math>ax^2+bx+c</math>. |
== Theorem == | == Theorem == | ||
| − | It states that if a [ | + | It states that if a [[quadratic equation]] <math>ax^2+bx+c</math> is divided by <math>x</math> then it gives the answer as an [[Integer]] if and only if <math>x </math> is equal to 1, [[Integer_factorization|Prime Factors]] and [[composite]] [[divisor]] of the constant <math>c</math> . |
| − | + | <math>\frac{ax^2+bx+c}{x} \in Z </math> Iff <math>x</math> is a factor of <math>c</math> where <math>a,b,c \in Z </math>. | |
| − | |||
| − | <math>\frac{ax^2+bx+c}{x} \in Z </math> Iff <math>x | ||
== Historical Note == | == Historical Note == | ||
| − | [ | + | [[Jyotiraditya Jadhav]] is a school student and is always curious about [https://www.ck12.org/book/ck-12-middle-school-math-concepts-grade-7/section/1.2 numerical patterns] which fall under the branch of [[Number Theory]]. He formulated many [https://en.wikipedia.org/wiki/Arithmetic arithmetic based equations] before too like [[Jadhav Theorem]], [[Jadhav Triads]], [[Jadhav Arithmetic Merging Equation]] and many more. While he was solving a question relating to [[quadratic equation]]s he found out this numerical pattern and organized the [[theorem]] over it. |
| − | == | + | == Proof == |
Now let us take <math>\frac{ax^2+bx+c}{x} </math> written as <math>\frac{x[ax+b]+c}{x} </math> | Now let us take <math>\frac{ax^2+bx+c}{x} </math> written as <math>\frac{x[ax+b]+c}{x} </math> | ||
| Line 20: | Line 18: | ||
'''Original Research paper''' can be found [https://issuu.com/jyotiraditya123/docs/jadhav_prime_quadratic_theorem here on Issuu] | '''Original Research paper''' can be found [https://issuu.com/jyotiraditya123/docs/jadhav_prime_quadratic_theorem here on Issuu] | ||
| − | + | {{delete|lacks notability}} | |
Revision as of 16:51, 14 February 2025
In Mathematics, Jadhav's Prime Quadratic Theorem is based on Algebra and Number Theory. Discovered by an Indian Mathematician Jyotiraditya Jadhav. Stating a condition over the value of 
in the quadratic equation 
.
Theorem
It states that if a quadratic equation is divided by then it gives the answer as an Integer if and only if is equal to 1, Prime Factors and composite divisor of the constant 
.
Iff is a factor of where 
.
Historical Note
Jyotiraditya Jadhav is a school student and is always curious about numerical patterns which fall under the branch of Number Theory. He formulated many arithmetic based equations before too like Jadhav Theorem, Jadhav Triads, Jadhav Arithmetic Merging Equation and many more. While he was solving a question relating to quadratic equations he found out this numerical pattern and organized the theorem over it.
Proof
Now let us take 
written as ![$\frac{x[ax+b]+c}{x}$](http://latex.artofproblemsolving.com/b/6/8/b6867beca66c17e4b64e51865f9912bba1c97256.png)
To cancel out from the denominator we need in numerator and to take as common from whole quadratic equation we need to have as a composite number made up as prime-factors with at least one factor as or in other words should be a multiple of and hence telling us should at least be a prime factor, composite divisor or 1 to give the answer as an Integer.
Hence Proving Jadhav Prime Quadratic Theorem.
Original Research paper can be found here on Issuu
| This article has been proposed for deletion. The reason given is: lacks notability
Sysops: Before deleting this article, please check the article discussion pages and history. |
